Will 275/40/20 fit on the front of a 05?

It probably could but without knowing the offset and such there's no way of knowing. Also I wouldn't recommend that tire size because you'd be rolling 5.2% slower then the standard size. You should always keep your plus sizing rev per mile rotation within 4% of the stock size or else you can throw off important systems like ABS or even cause some parts to fail.
 
That is a 28.7" tall tire. I wouldn't put it up front unless you plan on staying stock suspension! My rear tire is 28.3" tall and I would love to have another .4" in height back there, but up front????? The width is fine up front as the Roush TrakPak runs 275/40-18s on all four corners, but is 2" shorter than the tire you mentioned.
 
My calculations show that to have the closest match to a stock diameter on a 20 inch wheel you'd have to have 255/35/20's up front and 275/35/20 or 295/30/20s in the back. (these are math computations they don't reflect wheel/fender/suspension clearing)
 
With a tire that wide on the front (275) every groove and other road imperfections will feed back to the steering wheel making driving your car less fun and more of a chore. The widest I recommend is 255's for the front.
I have 275-35-19s on the front and rear, nine and ten inch rims, and what you say is true to a limited extent: at slow speeds in light braking conditions, they do "tramline". With higher speeds and stronger inputs, not so much. That is my experience with Michelin Pilot Sport PS2s at 275-35-19. With power steering, no big problem.

Of course there is the matter of tire construction, too. One of the characteristics in which reviewers see differences among brands, constructions, tread design, etc., is tramlining (used to be "nibble", didn't it?). Some are better than others in each parameter. TireRack.com has comparison tests where they talk about that kind of thing.

I haven't found any conditions that make driving my Mustang a chore.
:shrug: